• A variant of Metropolis Hastings algorithm
• More general and more efficient than standard Metropolis – uses fewer steps to get a good estimate of the posterior distribution
• Uses adaptive proposals:
• • o The proposed parameter values adjust intelligently, depending upon the current values.
• • o Uses conjugate pairs to compute adaptive proposals (prior distributions and likelihoods)

Limitations:

• Becomes very inefficient as the models become more complex.
• The model getting stuck in regions of high correlation in the posterior. Complex models often have highly correlated parameters, these parameters cause a narrow ridge of high probability combinations – thus the model will get stuck in these regions for a long time.
• Concentration of Measure - Any Markov chain approach that samples individual parameters in individual steps is going to get stuck, once the number of parameters grows sufficiently large.